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The descent of biquaternion algebras in characteristic two

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Abstract

In this paper we associate an invariant to a biquaternion algebra B over a field K with a subfield F such that K/F is a quadratic separable extension and char(F) = 2. We show that this invariant is trivial exactly when B ≅ B0 ⊗ K for some biquaternion algebra B0 over F. We also study the behavior of this invariant under certain field extensions and provide several interesting examples.

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Acknowledgements

The authors would like to thank Jean-Pierre Tignol for the discussions and the words of advice all along this project, and Nikita Karpenko for his help with writing the appendix. The authors also thank the anonymous referees for the helpful remarks on the submitted version.

The first author would like to thank the third author and Universite d’Artois for their support and hospitality (in 2017) while a part of the work for this paper was done. He gratefully acknowledges support from the FWO Odysseus Programme (project Explicit Methods in Quadratic Form Theory).

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Authors and Affiliations

  1. Faculté des Sciences et Techniques de Bamako, BP: E3206, Bamako, Mali

    Demba Barry

  2. Departement Wiskunde–Informatica, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Demba Barry

  3. Department of Computer Science, Tel-Hai College, Upper Galilee, 12208, Israel

    Adam Chapman

  4. Université d’Artois, Laboratoire de mathématiques de Lens—UR 2462, rue Jean Souvraz — SP18, 62307, Lens, France

    Ahmed Laghribi

Authors
  1. Demba Barry
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  2. Adam Chapman
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  3. Ahmed Laghribi
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Correspondence to Ahmed Laghribi.

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Barry, D., Chapman, A. & Laghribi, A. The descent of biquaternion algebras in characteristic two. Isr. J. Math. 235, 295–323 (2020). https://doi.org/10.1007/s11856-019-1958-3

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  • DOI: https://doi.org/10.1007/s11856-019-1958-3

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